Properties

Label 630.2.bk.a.101.1
Level 630
Weight 2
Character 630.101
Analytic conductor 5.031
Analytic rank 1
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.bk (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.03057532734\)
Analytic rank: \(1\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.1
Root \(0.866025 - 0.500000i\) of \(x^{4} - x^{2} + 1\)
Character \(\chi\) \(=\) 630.101
Dual form 630.2.bk.a.131.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(0.866025 - 1.50000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(0.866025 - 1.50000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(0.866025 + 0.500000i) q^{10} +(-4.09808 + 2.36603i) q^{11} +(-0.866025 + 1.50000i) q^{12} +(-3.00000 + 1.73205i) q^{13} +(0.866025 + 2.50000i) q^{14} +(0.866025 + 1.50000i) q^{15} +1.00000 q^{16} +(-2.59808 + 1.50000i) q^{18} +(-1.09808 + 0.633975i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.866025 + 4.50000i) q^{21} +(2.36603 + 4.09808i) q^{22} +(2.19615 + 1.26795i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.73205 + 3.00000i) q^{26} -5.19615 q^{27} +(2.50000 - 0.866025i) q^{28} +(-5.59808 - 3.23205i) q^{29} +(1.50000 - 0.866025i) q^{30} -8.19615i q^{31} -1.00000i q^{32} +8.19615i q^{33} +(0.500000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{36} +(-3.09808 - 5.36603i) q^{37} +(0.633975 + 1.09808i) q^{38} +6.00000i q^{39} +(-0.866025 - 0.500000i) q^{40} +(4.50000 + 7.79423i) q^{41} +(4.50000 + 0.866025i) q^{42} +(-1.59808 + 2.76795i) q^{43} +(4.09808 - 2.36603i) q^{44} +3.00000 q^{45} +(1.26795 - 2.19615i) q^{46} -9.00000 q^{47} +(0.866025 - 1.50000i) q^{48} +(5.50000 - 4.33013i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(3.00000 - 1.73205i) q^{52} +(6.29423 + 3.63397i) q^{53} +5.19615i q^{54} -4.73205i q^{55} +(-0.866025 - 2.50000i) q^{56} +2.19615i q^{57} +(-3.23205 + 5.59808i) q^{58} +2.19615 q^{59} +(-0.866025 - 1.50000i) q^{60} -12.9282i q^{61} -8.19615 q^{62} +(6.00000 + 5.19615i) q^{63} -1.00000 q^{64} -3.46410i q^{65} +8.19615 q^{66} -4.00000 q^{67} +(3.80385 - 2.19615i) q^{69} +(-2.59808 - 0.500000i) q^{70} +4.73205i q^{71} +(2.59808 - 1.50000i) q^{72} +(6.00000 + 3.46410i) q^{73} +(-5.36603 + 3.09808i) q^{74} -1.73205 q^{75} +(1.09808 - 0.633975i) q^{76} +(8.19615 - 9.46410i) q^{77} +6.00000 q^{78} +14.5885 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(7.79423 - 4.50000i) q^{82} +(-5.59808 + 9.69615i) q^{83} +(0.866025 - 4.50000i) q^{84} +(2.76795 + 1.59808i) q^{86} +(-9.69615 + 5.59808i) q^{87} +(-2.36603 - 4.09808i) q^{88} +(2.19615 + 3.80385i) q^{89} -3.00000i q^{90} +(6.00000 - 6.92820i) q^{91} +(-2.19615 - 1.26795i) q^{92} +(-12.2942 - 7.09808i) q^{93} +9.00000i q^{94} -1.26795i q^{95} +(-1.50000 - 0.866025i) q^{96} +(-7.39230 - 4.26795i) q^{97} +(-4.33013 - 5.50000i) q^{98} +(12.2942 + 7.09808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{4} - 2q^{5} - 6q^{6} - 10q^{7} - 6q^{9} + O(q^{10}) \) \( 4q - 4q^{4} - 2q^{5} - 6q^{6} - 10q^{7} - 6q^{9} - 6q^{11} - 12q^{13} + 4q^{16} + 6q^{19} + 2q^{20} + 6q^{22} - 12q^{23} + 6q^{24} - 2q^{25} + 10q^{28} - 12q^{29} + 6q^{30} + 2q^{35} + 6q^{36} - 2q^{37} + 6q^{38} + 18q^{41} + 18q^{42} + 4q^{43} + 6q^{44} + 12q^{45} + 12q^{46} - 36q^{47} + 22q^{49} + 12q^{52} - 6q^{53} - 6q^{58} - 12q^{59} - 12q^{62} + 24q^{63} - 4q^{64} + 12q^{66} - 16q^{67} + 36q^{69} + 24q^{73} - 18q^{74} - 6q^{76} + 12q^{77} + 24q^{78} - 4q^{79} - 2q^{80} - 18q^{81} - 12q^{83} + 18q^{86} - 18q^{87} - 6q^{88} - 12q^{89} + 24q^{91} + 12q^{92} - 18q^{93} - 6q^{96} + 12q^{97} + 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.866025 1.50000i 0.500000 0.866025i
\(4\) −1.00000 −0.500000
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) −1.50000 0.866025i −0.612372 0.353553i
\(7\) −2.50000 + 0.866025i −0.944911 + 0.327327i
\(8\) 1.00000i 0.353553i
\(9\) −1.50000 2.59808i −0.500000 0.866025i
\(10\) 0.866025 + 0.500000i 0.273861 + 0.158114i
\(11\) −4.09808 + 2.36603i −1.23562 + 0.713384i −0.968195 0.250196i \(-0.919505\pi\)
−0.267421 + 0.963580i \(0.586172\pi\)
\(12\) −0.866025 + 1.50000i −0.250000 + 0.433013i
\(13\) −3.00000 + 1.73205i −0.832050 + 0.480384i −0.854554 0.519362i \(-0.826170\pi\)
0.0225039 + 0.999747i \(0.492836\pi\)
\(14\) 0.866025 + 2.50000i 0.231455 + 0.668153i
\(15\) 0.866025 + 1.50000i 0.223607 + 0.387298i
\(16\) 1.00000 0.250000
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) −2.59808 + 1.50000i −0.612372 + 0.353553i
\(19\) −1.09808 + 0.633975i −0.251916 + 0.145444i −0.620641 0.784095i \(-0.713128\pi\)
0.368725 + 0.929538i \(0.379794\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) −0.866025 + 4.50000i −0.188982 + 0.981981i
\(22\) 2.36603 + 4.09808i 0.504438 + 0.873713i
\(23\) 2.19615 + 1.26795i 0.457929 + 0.264386i 0.711173 0.703017i \(-0.248164\pi\)
−0.253244 + 0.967402i \(0.581497\pi\)
\(24\) 1.50000 + 0.866025i 0.306186 + 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 1.73205 + 3.00000i 0.339683 + 0.588348i
\(27\) −5.19615 −1.00000
\(28\) 2.50000 0.866025i 0.472456 0.163663i
\(29\) −5.59808 3.23205i −1.03954 0.600177i −0.119835 0.992794i \(-0.538236\pi\)
−0.919702 + 0.392617i \(0.871570\pi\)
\(30\) 1.50000 0.866025i 0.273861 0.158114i
\(31\) 8.19615i 1.47207i −0.676942 0.736036i \(-0.736695\pi\)
0.676942 0.736036i \(-0.263305\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 8.19615i 1.42677i
\(34\) 0 0
\(35\) 0.500000 2.59808i 0.0845154 0.439155i
\(36\) 1.50000 + 2.59808i 0.250000 + 0.433013i
\(37\) −3.09808 5.36603i −0.509321 0.882169i −0.999942 0.0107961i \(-0.996563\pi\)
0.490621 0.871373i \(-0.336770\pi\)
\(38\) 0.633975 + 1.09808i 0.102844 + 0.178131i
\(39\) 6.00000i 0.960769i
\(40\) −0.866025 0.500000i −0.136931 0.0790569i
\(41\) 4.50000 + 7.79423i 0.702782 + 1.21725i 0.967486 + 0.252924i \(0.0813924\pi\)
−0.264704 + 0.964330i \(0.585274\pi\)
\(42\) 4.50000 + 0.866025i 0.694365 + 0.133631i
\(43\) −1.59808 + 2.76795i −0.243704 + 0.422108i −0.961767 0.273871i \(-0.911696\pi\)
0.718062 + 0.695979i \(0.245029\pi\)
\(44\) 4.09808 2.36603i 0.617808 0.356692i
\(45\) 3.00000 0.447214
\(46\) 1.26795 2.19615i 0.186949 0.323805i
\(47\) −9.00000 −1.31278 −0.656392 0.754420i \(-0.727918\pi\)
−0.656392 + 0.754420i \(0.727918\pi\)
\(48\) 0.866025 1.50000i 0.125000 0.216506i
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) −0.866025 + 0.500000i −0.122474 + 0.0707107i
\(51\) 0 0
\(52\) 3.00000 1.73205i 0.416025 0.240192i
\(53\) 6.29423 + 3.63397i 0.864579 + 0.499165i 0.865543 0.500835i \(-0.166974\pi\)
−0.000964138 1.00000i \(0.500307\pi\)
\(54\) 5.19615i 0.707107i
\(55\) 4.73205i 0.638070i
\(56\) −0.866025 2.50000i −0.115728 0.334077i
\(57\) 2.19615i 0.290887i
\(58\) −3.23205 + 5.59808i −0.424389 + 0.735063i
\(59\) 2.19615 0.285915 0.142957 0.989729i \(-0.454339\pi\)
0.142957 + 0.989729i \(0.454339\pi\)
\(60\) −0.866025 1.50000i −0.111803 0.193649i
\(61\) 12.9282i 1.65529i −0.561254 0.827643i \(-0.689681\pi\)
0.561254 0.827643i \(-0.310319\pi\)
\(62\) −8.19615 −1.04091
\(63\) 6.00000 + 5.19615i 0.755929 + 0.654654i
\(64\) −1.00000 −0.125000
\(65\) 3.46410i 0.429669i
\(66\) 8.19615 1.00888
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) 3.80385 2.19615i 0.457929 0.264386i
\(70\) −2.59808 0.500000i −0.310530 0.0597614i
\(71\) 4.73205i 0.561591i 0.959768 + 0.280796i \(0.0905983\pi\)
−0.959768 + 0.280796i \(0.909402\pi\)
\(72\) 2.59808 1.50000i 0.306186 0.176777i
\(73\) 6.00000 + 3.46410i 0.702247 + 0.405442i 0.808184 0.588930i \(-0.200451\pi\)
−0.105937 + 0.994373i \(0.533784\pi\)
\(74\) −5.36603 + 3.09808i −0.623788 + 0.360144i
\(75\) −1.73205 −0.200000
\(76\) 1.09808 0.633975i 0.125958 0.0727219i
\(77\) 8.19615 9.46410i 0.934038 1.07853i
\(78\) 6.00000 0.679366
\(79\) 14.5885 1.64133 0.820665 0.571410i \(-0.193603\pi\)
0.820665 + 0.571410i \(0.193603\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 7.79423 4.50000i 0.860729 0.496942i
\(83\) −5.59808 + 9.69615i −0.614469 + 1.06429i 0.376009 + 0.926616i \(0.377296\pi\)
−0.990477 + 0.137675i \(0.956037\pi\)
\(84\) 0.866025 4.50000i 0.0944911 0.490990i
\(85\) 0 0
\(86\) 2.76795 + 1.59808i 0.298476 + 0.172325i
\(87\) −9.69615 + 5.59808i −1.03954 + 0.600177i
\(88\) −2.36603 4.09808i −0.252219 0.436856i
\(89\) 2.19615 + 3.80385i 0.232792 + 0.403207i 0.958629 0.284660i \(-0.0918806\pi\)
−0.725837 + 0.687867i \(0.758547\pi\)
\(90\) 3.00000i 0.316228i
\(91\) 6.00000 6.92820i 0.628971 0.726273i
\(92\) −2.19615 1.26795i −0.228965 0.132193i
\(93\) −12.2942 7.09808i −1.27485 0.736036i
\(94\) 9.00000i 0.928279i
\(95\) 1.26795i 0.130089i
\(96\) −1.50000 0.866025i −0.153093 0.0883883i
\(97\) −7.39230 4.26795i −0.750575 0.433345i 0.0753267 0.997159i \(-0.476000\pi\)
−0.825902 + 0.563814i \(0.809333\pi\)
\(98\) −4.33013 5.50000i −0.437409 0.555584i
\(99\) 12.2942 + 7.09808i 1.23562 + 0.713384i
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) −5.59808 9.69615i −0.557029 0.964803i −0.997743 0.0671552i \(-0.978608\pi\)
0.440713 0.897648i \(-0.354726\pi\)
\(102\) 0 0
\(103\) −10.5000 6.06218i −1.03460 0.597324i −0.116298 0.993214i \(-0.537103\pi\)
−0.918298 + 0.395890i \(0.870436\pi\)
\(104\) −1.73205 3.00000i −0.169842 0.294174i
\(105\) −3.46410 3.00000i −0.338062 0.292770i
\(106\) 3.63397 6.29423i 0.352963 0.611350i
\(107\) −13.7942 + 7.96410i −1.33354 + 0.769919i −0.985840 0.167688i \(-0.946370\pi\)
−0.347698 + 0.937606i \(0.613037\pi\)
\(108\) 5.19615 0.500000
\(109\) 3.59808 6.23205i 0.344633 0.596922i −0.640654 0.767830i \(-0.721337\pi\)
0.985287 + 0.170908i \(0.0546700\pi\)
\(110\) −4.73205 −0.451183
\(111\) −10.7321 −1.01864
\(112\) −2.50000 + 0.866025i −0.236228 + 0.0818317i
\(113\) −10.9019 + 6.29423i −1.02557 + 0.592111i −0.915711 0.401836i \(-0.868372\pi\)
−0.109855 + 0.993948i \(0.535039\pi\)
\(114\) 2.19615 0.205689
\(115\) −2.19615 + 1.26795i −0.204792 + 0.118237i
\(116\) 5.59808 + 3.23205i 0.519768 + 0.300088i
\(117\) 9.00000 + 5.19615i 0.832050 + 0.480384i
\(118\) 2.19615i 0.202172i
\(119\) 0 0
\(120\) −1.50000 + 0.866025i −0.136931 + 0.0790569i
\(121\) 5.69615 9.86603i 0.517832 0.896911i
\(122\) −12.9282 −1.17046
\(123\) 15.5885 1.40556
\(124\) 8.19615i 0.736036i
\(125\) 1.00000 0.0894427
\(126\) 5.19615 6.00000i 0.462910 0.534522i
\(127\) −11.3923 −1.01090 −0.505452 0.862855i \(-0.668674\pi\)
−0.505452 + 0.862855i \(0.668674\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 2.76795 + 4.79423i 0.243704 + 0.422108i
\(130\) −3.46410 −0.303822
\(131\) 2.19615 3.80385i 0.191879 0.332344i −0.753994 0.656881i \(-0.771875\pi\)
0.945873 + 0.324537i \(0.105209\pi\)
\(132\) 8.19615i 0.713384i
\(133\) 2.19615 2.53590i 0.190431 0.219890i
\(134\) 4.00000i 0.345547i
\(135\) 2.59808 4.50000i 0.223607 0.387298i
\(136\) 0 0
\(137\) 6.29423 3.63397i 0.537752 0.310471i −0.206415 0.978464i \(-0.566180\pi\)
0.744167 + 0.667993i \(0.232846\pi\)
\(138\) −2.19615 3.80385i −0.186949 0.323805i
\(139\) −19.0981 + 11.0263i −1.61988 + 0.935237i −0.632927 + 0.774211i \(0.718147\pi\)
−0.986950 + 0.161026i \(0.948520\pi\)
\(140\) −0.500000 + 2.59808i −0.0422577 + 0.219578i
\(141\) −7.79423 + 13.5000i −0.656392 + 1.13691i
\(142\) 4.73205 0.397105
\(143\) 8.19615 14.1962i 0.685397 1.18714i
\(144\) −1.50000 2.59808i −0.125000 0.216506i
\(145\) 5.59808 3.23205i 0.464895 0.268407i
\(146\) 3.46410 6.00000i 0.286691 0.496564i
\(147\) −1.73205 12.0000i −0.142857 0.989743i
\(148\) 3.09808 + 5.36603i 0.254660 + 0.441085i
\(149\) 10.3923 + 6.00000i 0.851371 + 0.491539i 0.861113 0.508413i \(-0.169768\pi\)
−0.00974235 + 0.999953i \(0.503101\pi\)
\(150\) 1.73205i 0.141421i
\(151\) 2.09808 + 3.63397i 0.170739 + 0.295729i 0.938678 0.344794i \(-0.112051\pi\)
−0.767939 + 0.640522i \(0.778718\pi\)
\(152\) −0.633975 1.09808i −0.0514221 0.0890657i
\(153\) 0 0
\(154\) −9.46410 8.19615i −0.762639 0.660465i
\(155\) 7.09808 + 4.09808i 0.570131 + 0.329165i
\(156\) 6.00000i 0.480384i
\(157\) 17.6603i 1.40944i −0.709485 0.704721i \(-0.751072\pi\)
0.709485 0.704721i \(-0.248928\pi\)
\(158\) 14.5885i 1.16060i
\(159\) 10.9019 6.29423i 0.864579 0.499165i
\(160\) 0.866025 + 0.500000i 0.0684653 + 0.0395285i
\(161\) −6.58846 1.26795i −0.519243 0.0999284i
\(162\) 7.79423 + 4.50000i 0.612372 + 0.353553i
\(163\) 4.19615 + 7.26795i 0.328668 + 0.569270i 0.982248 0.187588i \(-0.0600669\pi\)
−0.653580 + 0.756858i \(0.726734\pi\)
\(164\) −4.50000 7.79423i −0.351391 0.608627i
\(165\) −7.09808 4.09808i −0.552584 0.319035i
\(166\) 9.69615 + 5.59808i 0.752567 + 0.434495i
\(167\) −5.19615 9.00000i −0.402090 0.696441i 0.591888 0.806020i \(-0.298383\pi\)
−0.993978 + 0.109580i \(0.965050\pi\)
\(168\) −4.50000 0.866025i −0.347183 0.0668153i
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) 0 0
\(171\) 3.29423 + 1.90192i 0.251916 + 0.145444i
\(172\) 1.59808 2.76795i 0.121852 0.211054i
\(173\) 8.19615 0.623142 0.311571 0.950223i \(-0.399145\pi\)
0.311571 + 0.950223i \(0.399145\pi\)
\(174\) 5.59808 + 9.69615i 0.424389 + 0.735063i
\(175\) 2.00000 + 1.73205i 0.151186 + 0.130931i
\(176\) −4.09808 + 2.36603i −0.308904 + 0.178346i
\(177\) 1.90192 3.29423i 0.142957 0.247609i
\(178\) 3.80385 2.19615i 0.285110 0.164609i
\(179\) −21.2942 12.2942i −1.59161 0.918914i −0.993032 0.117846i \(-0.962401\pi\)
−0.598573 0.801068i \(-0.704266\pi\)
\(180\) −3.00000 −0.223607
\(181\) 13.3923i 0.995442i −0.867337 0.497721i \(-0.834170\pi\)
0.867337 0.497721i \(-0.165830\pi\)
\(182\) −6.92820 6.00000i −0.513553 0.444750i
\(183\) −19.3923 11.1962i −1.43352 0.827643i
\(184\) −1.26795 + 2.19615i −0.0934745 + 0.161903i
\(185\) 6.19615 0.455550
\(186\) −7.09808 + 12.2942i −0.520456 + 0.901457i
\(187\) 0 0
\(188\) 9.00000 0.656392
\(189\) 12.9904 4.50000i 0.944911 0.327327i
\(190\) −1.26795 −0.0919867
\(191\) 3.46410i 0.250654i 0.992116 + 0.125327i \(0.0399979\pi\)
−0.992116 + 0.125327i \(0.960002\pi\)
\(192\) −0.866025 + 1.50000i −0.0625000 + 0.108253i
\(193\) 13.8038 0.993623 0.496811 0.867859i \(-0.334504\pi\)
0.496811 + 0.867859i \(0.334504\pi\)
\(194\) −4.26795 + 7.39230i −0.306421 + 0.530737i
\(195\) −5.19615 3.00000i −0.372104 0.214834i
\(196\) −5.50000 + 4.33013i −0.392857 + 0.309295i
\(197\) 23.6603i 1.68572i 0.538130 + 0.842862i \(0.319131\pi\)
−0.538130 + 0.842862i \(0.680869\pi\)
\(198\) 7.09808 12.2942i 0.504438 0.873713i
\(199\) 6.00000 + 3.46410i 0.425329 + 0.245564i 0.697355 0.716726i \(-0.254360\pi\)
−0.272026 + 0.962290i \(0.587694\pi\)
\(200\) 0.866025 0.500000i 0.0612372 0.0353553i
\(201\) −3.46410 + 6.00000i −0.244339 + 0.423207i
\(202\) −9.69615 + 5.59808i −0.682219 + 0.393879i
\(203\) 16.7942 + 3.23205i 1.17872 + 0.226845i
\(204\) 0 0
\(205\) −9.00000 −0.628587
\(206\) −6.06218 + 10.5000i −0.422372 + 0.731570i
\(207\) 7.60770i 0.528771i
\(208\) −3.00000 + 1.73205i −0.208013 + 0.120096i
\(209\) 3.00000 5.19615i 0.207514 0.359425i
\(210\) −3.00000 + 3.46410i −0.207020 + 0.239046i
\(211\) 10.2942 + 17.8301i 0.708684 + 1.22748i 0.965345 + 0.260975i \(0.0840441\pi\)
−0.256662 + 0.966501i \(0.582623\pi\)
\(212\) −6.29423 3.63397i −0.432289 0.249582i
\(213\) 7.09808 + 4.09808i 0.486352 + 0.280796i
\(214\) 7.96410 + 13.7942i 0.544415 + 0.942954i
\(215\) −1.59808 2.76795i −0.108988 0.188773i
\(216\) 5.19615i 0.353553i
\(217\) 7.09808 + 20.4904i 0.481849 + 1.39098i
\(218\) −6.23205 3.59808i −0.422088 0.243692i
\(219\) 10.3923 6.00000i 0.702247 0.405442i
\(220\) 4.73205i 0.319035i
\(221\) 0 0
\(222\) 10.7321i 0.720288i
\(223\) −11.8923 6.86603i −0.796368 0.459783i 0.0458318 0.998949i \(-0.485406\pi\)
−0.842199 + 0.539166i \(0.818740\pi\)
\(224\) 0.866025 + 2.50000i 0.0578638 + 0.167038i
\(225\) −1.50000 + 2.59808i −0.100000 + 0.173205i
\(226\) 6.29423 + 10.9019i 0.418686 + 0.725185i
\(227\) −8.19615 14.1962i −0.543998 0.942232i −0.998669 0.0515725i \(-0.983577\pi\)
0.454672 0.890659i \(-0.349757\pi\)
\(228\) 2.19615i 0.145444i
\(229\) −12.1865 7.03590i −0.805309 0.464945i 0.0400153 0.999199i \(-0.487259\pi\)
−0.845324 + 0.534254i \(0.820593\pi\)
\(230\) 1.26795 + 2.19615i 0.0836061 + 0.144810i
\(231\) −7.09808 20.4904i −0.467019 1.34817i
\(232\) 3.23205 5.59808i 0.212195 0.367532i
\(233\) −1.09808 + 0.633975i −0.0719374 + 0.0415331i −0.535537 0.844512i \(-0.679891\pi\)
0.463600 + 0.886045i \(0.346558\pi\)
\(234\) 5.19615 9.00000i 0.339683 0.588348i
\(235\) 4.50000 7.79423i 0.293548 0.508439i
\(236\) −2.19615 −0.142957
\(237\) 12.6340 21.8827i 0.820665 1.42143i
\(238\) 0 0
\(239\) 2.70577 1.56218i 0.175022 0.101049i −0.409930 0.912117i \(-0.634447\pi\)
0.584952 + 0.811068i \(0.301113\pi\)
\(240\) 0.866025 + 1.50000i 0.0559017 + 0.0968246i
\(241\) 2.89230 1.66987i 0.186310 0.107566i −0.403944 0.914784i \(-0.632361\pi\)
0.590254 + 0.807218i \(0.299028\pi\)
\(242\) −9.86603 5.69615i −0.634212 0.366163i
\(243\) 7.79423 + 13.5000i 0.500000 + 0.866025i
\(244\) 12.9282i 0.827643i
\(245\) 1.00000 + 6.92820i 0.0638877 + 0.442627i
\(246\) 15.5885i 0.993884i
\(247\) 2.19615 3.80385i 0.139738 0.242033i
\(248\) 8.19615 0.520456
\(249\) 9.69615 + 16.7942i 0.614469 + 1.06429i
\(250\) 1.00000i 0.0632456i
\(251\) 18.0000 1.13615 0.568075 0.822977i \(-0.307688\pi\)
0.568075 + 0.822977i \(0.307688\pi\)
\(252\) −6.00000 5.19615i −0.377964 0.327327i
\(253\) −12.0000 −0.754434
\(254\) 11.3923i 0.714817i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 14.1962 24.5885i 0.885532 1.53379i 0.0404286 0.999182i \(-0.487128\pi\)
0.845103 0.534603i \(-0.179539\pi\)
\(258\) 4.79423 2.76795i 0.298476 0.172325i
\(259\) 12.3923 + 10.7321i 0.770020 + 0.666857i
\(260\) 3.46410i 0.214834i
\(261\) 19.3923i 1.20035i
\(262\) −3.80385 2.19615i −0.235002 0.135679i
\(263\) −11.8923 + 6.86603i −0.733311 + 0.423377i −0.819632 0.572890i \(-0.805822\pi\)
0.0863213 + 0.996267i \(0.472489\pi\)
\(264\) −8.19615 −0.504438
\(265\) −6.29423 + 3.63397i −0.386651 + 0.223233i
\(266\) −2.53590 2.19615i −0.155486 0.134655i
\(267\) 7.60770 0.465583
\(268\) 4.00000 0.244339
\(269\) −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i \(0.351559\pi\)
−0.998361 + 0.0572259i \(0.981774\pi\)
\(270\) −4.50000 2.59808i −0.273861 0.158114i
\(271\) 5.70577 3.29423i 0.346601 0.200110i −0.316586 0.948564i \(-0.602537\pi\)
0.663187 + 0.748454i \(0.269203\pi\)
\(272\) 0 0
\(273\) −5.19615 15.0000i −0.314485 0.907841i
\(274\) −3.63397 6.29423i −0.219536 0.380248i
\(275\) 4.09808 + 2.36603i 0.247123 + 0.142677i
\(276\) −3.80385 + 2.19615i −0.228965 + 0.132193i
\(277\) 12.0981 + 20.9545i 0.726903 + 1.25903i 0.958186 + 0.286146i \(0.0923743\pi\)
−0.231283 + 0.972887i \(0.574292\pi\)
\(278\) 11.0263 + 19.0981i 0.661312 + 1.14543i
\(279\) −21.2942 + 12.2942i −1.27485 + 0.736036i
\(280\) 2.59808 + 0.500000i 0.155265 + 0.0298807i
\(281\) 12.6962 + 7.33013i 0.757389 + 0.437279i 0.828357 0.560200i \(-0.189276\pi\)
−0.0709685 + 0.997479i \(0.522609\pi\)
\(282\) 13.5000 + 7.79423i 0.803913 + 0.464140i
\(283\) 16.8564i 1.00201i −0.865445 0.501005i \(-0.832964\pi\)
0.865445 0.501005i \(-0.167036\pi\)
\(284\) 4.73205i 0.280796i
\(285\) −1.90192 1.09808i −0.112660 0.0650444i
\(286\) −14.1962 8.19615i −0.839436 0.484649i
\(287\) −18.0000 15.5885i −1.06251 0.920158i
\(288\) −2.59808 + 1.50000i −0.153093 + 0.0883883i
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −3.23205 5.59808i −0.189793 0.328730i
\(291\) −12.8038 + 7.39230i −0.750575 + 0.433345i
\(292\) −6.00000 3.46410i −0.351123 0.202721i
\(293\) 8.19615 + 14.1962i 0.478824 + 0.829348i 0.999705 0.0242813i \(-0.00772975\pi\)
−0.520881 + 0.853629i \(0.674396\pi\)
\(294\) −12.0000 + 1.73205i −0.699854 + 0.101015i
\(295\) −1.09808 + 1.90192i −0.0639325 + 0.110734i
\(296\) 5.36603 3.09808i 0.311894 0.180072i
\(297\) 21.2942 12.2942i 1.23562 0.713384i
\(298\) 6.00000 10.3923i 0.347571 0.602010i
\(299\) −8.78461 −0.508027
\(300\) 1.73205 0.100000
\(301\) 1.59808 8.30385i 0.0921116 0.478626i
\(302\) 3.63397 2.09808i 0.209112 0.120731i
\(303\) −19.3923 −1.11406
\(304\) −1.09808 + 0.633975i −0.0629790 + 0.0363609i
\(305\) 11.1962 + 6.46410i 0.641090 + 0.370133i
\(306\) 0 0
\(307\) 23.7846i 1.35746i 0.734388 + 0.678730i \(0.237469\pi\)
−0.734388 + 0.678730i \(0.762531\pi\)
\(308\) −8.19615 + 9.46410i −0.467019 + 0.539267i
\(309\) −18.1865 + 10.5000i −1.03460 + 0.597324i
\(310\) 4.09808 7.09808i 0.232755 0.403144i
\(311\) −15.8038 −0.896154 −0.448077 0.893995i \(-0.647891\pi\)
−0.448077 + 0.893995i \(0.647891\pi\)
\(312\) −6.00000 −0.339683
\(313\) 20.1962i 1.14155i 0.821105 + 0.570777i \(0.193358\pi\)
−0.821105 + 0.570777i \(0.806642\pi\)
\(314\) −17.6603 −0.996626
\(315\) −7.50000 + 2.59808i −0.422577 + 0.146385i
\(316\) −14.5885 −0.820665
\(317\) 20.5359i 1.15341i 0.816952 + 0.576705i \(0.195662\pi\)
−0.816952 + 0.576705i \(0.804338\pi\)
\(318\) −6.29423 10.9019i −0.352963 0.611350i
\(319\) 30.5885 1.71262
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) 27.5885i 1.53984i
\(322\) −1.26795 + 6.58846i −0.0706600 + 0.367160i
\(323\) 0 0
\(324\) 4.50000 7.79423i 0.250000 0.433013i
\(325\) 3.00000 + 1.73205i 0.166410 + 0.0960769i
\(326\) 7.26795 4.19615i 0.402534 0.232403i
\(327\) −6.23205 10.7942i −0.344633 0.596922i
\(328\) −7.79423 + 4.50000i −0.430364 + 0.248471i
\(329\) 22.5000 7.79423i 1.24047 0.429710i
\(330\) −4.09808 + 7.09808i −0.225592 + 0.390736i
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 5.59808 9.69615i 0.307234 0.532145i
\(333\) −9.29423 + 16.0981i −0.509321 + 0.882169i
\(334\) −9.00000 + 5.19615i −0.492458 + 0.284321i
\(335\) 2.00000 3.46410i 0.109272 0.189264i
\(336\) −0.866025 + 4.50000i −0.0472456 + 0.245495i
\(337\) −5.00000 8.66025i −0.272367 0.471754i 0.697100 0.716974i \(-0.254473\pi\)
−0.969468 + 0.245220i \(0.921140\pi\)
\(338\) 0.866025 + 0.500000i 0.0471056 + 0.0271964i
\(339\) 21.8038i 1.18422i
\(340\) 0 0
\(341\) 19.3923 + 33.5885i 1.05015 + 1.81892i
\(342\) 1.90192 3.29423i 0.102844 0.178131i
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) −2.76795 1.59808i −0.149238 0.0861625i
\(345\) 4.39230i 0.236474i
\(346\) 8.19615i 0.440628i
\(347\) 21.2487i 1.14069i −0.821405 0.570345i \(-0.806809\pi\)
0.821405 0.570345i \(-0.193191\pi\)
\(348\) 9.69615 5.59808i 0.519768 0.300088i
\(349\) −14.1962 8.19615i −0.759903 0.438730i 0.0693582 0.997592i \(-0.477905\pi\)
−0.829261 + 0.558862i \(0.811238\pi\)
\(350\) 1.73205 2.00000i 0.0925820 0.106904i
\(351\) 15.5885 9.00000i 0.832050 0.480384i
\(352\) 2.36603 + 4.09808i 0.126110 + 0.218428i
\(353\) −0.294229 0.509619i −0.0156602 0.0271243i 0.858089 0.513501i \(-0.171652\pi\)
−0.873749 + 0.486377i \(0.838318\pi\)
\(354\) −3.29423 1.90192i −0.175086 0.101086i
\(355\) −4.09808 2.36603i −0.217503 0.125576i
\(356\) −2.19615 3.80385i −0.116396 0.201604i
\(357\) 0 0
\(358\) −12.2942 + 21.2942i −0.649770 + 1.12543i
\(359\) 13.6865 7.90192i 0.722348 0.417048i −0.0932685 0.995641i \(-0.529732\pi\)
0.815616 + 0.578593i \(0.196398\pi\)
\(360\) 3.00000i 0.158114i
\(361\) −8.69615 + 15.0622i −0.457692 + 0.792746i
\(362\) −13.3923 −0.703884
\(363\) −9.86603 17.0885i −0.517832 0.896911i
\(364\) −6.00000 + 6.92820i −0.314485 + 0.363137i
\(365\) −6.00000 + 3.46410i −0.314054 + 0.181319i
\(366\) −11.1962 + 19.3923i −0.585232 + 1.01365i
\(367\) −25.2846 + 14.5981i −1.31985 + 0.762013i −0.983704 0.179798i \(-0.942456\pi\)
−0.336142 + 0.941811i \(0.609122\pi\)
\(368\) 2.19615 + 1.26795i 0.114482 + 0.0660964i
\(369\) 13.5000 23.3827i 0.702782 1.21725i
\(370\) 6.19615i 0.322123i
\(371\) −18.8827 3.63397i −0.980340 0.188667i
\(372\) 12.2942 + 7.09808i 0.637426 + 0.368018i
\(373\) −5.09808 + 8.83013i −0.263968 + 0.457207i −0.967293 0.253662i \(-0.918365\pi\)
0.703324 + 0.710869i \(0.251698\pi\)
\(374\) 0 0
\(375\) 0.866025 1.50000i 0.0447214 0.0774597i
\(376\) 9.00000i 0.464140i
\(377\) 22.3923 1.15326
\(378\) −4.50000 12.9904i −0.231455 0.668153i
\(379\) −9.60770 −0.493514 −0.246757 0.969077i \(-0.579365\pi\)
−0.246757 + 0.969077i \(0.579365\pi\)
\(380\) 1.26795i 0.0650444i
\(381\) −9.86603 + 17.0885i −0.505452 + 0.875468i
\(382\) 3.46410 0.177239
\(383\) 9.69615 16.7942i 0.495450 0.858145i −0.504536 0.863391i \(-0.668336\pi\)
0.999986 + 0.00524566i \(0.00166975\pi\)
\(384\) 1.50000 + 0.866025i 0.0765466 + 0.0441942i
\(385\) 4.09808 + 11.8301i 0.208857 + 0.602919i
\(386\) 13.8038i 0.702597i
\(387\) 9.58846 0.487409
\(388\) 7.39230 + 4.26795i 0.375287 + 0.216672i
\(389\) 21.4019 12.3564i 1.08512 0.626495i 0.152847 0.988250i \(-0.451156\pi\)
0.932273 + 0.361755i \(0.117822\pi\)
\(390\) −3.00000 + 5.19615i −0.151911 + 0.263117i
\(391\) 0 0
\(392\) 4.33013 + 5.50000i 0.218704 + 0.277792i
\(393\) −3.80385 6.58846i −0.191879 0.332344i
\(394\) 23.6603 1.19199
\(395\) −7.29423 + 12.6340i −0.367012 + 0.635684i
\(396\) −12.2942 7.09808i −0.617808 0.356692i
\(397\) −26.4904 + 15.2942i −1.32951 + 0.767595i −0.985224 0.171268i \(-0.945214\pi\)
−0.344290 + 0.938863i \(0.611880\pi\)
\(398\) 3.46410 6.00000i 0.173640 0.300753i
\(399\) −1.90192 5.49038i −0.0952153 0.274863i
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 3.10770 + 1.79423i 0.155191 + 0.0895995i 0.575584 0.817742i \(-0.304775\pi\)
−0.420393 + 0.907342i \(0.638108\pi\)
\(402\) 6.00000 + 3.46410i 0.299253 + 0.172774i
\(403\) 14.1962 + 24.5885i 0.707161 + 1.22484i
\(404\) 5.59808 + 9.69615i 0.278515 + 0.482402i
\(405\) −4.50000 7.79423i −0.223607 0.387298i
\(406\) 3.23205 16.7942i 0.160404 0.833484i
\(407\) 25.3923 + 14.6603i 1.25865 + 0.726682i
\(408\) 0 0
\(409\) 10.5167i 0.520015i −0.965607 0.260008i \(-0.916275\pi\)
0.965607 0.260008i \(-0.0837251\pi\)
\(410\) 9.00000i 0.444478i
\(411\) 12.5885i 0.620943i
\(412\) 10.5000 + 6.06218i 0.517298 + 0.298662i
\(413\) −5.49038 + 1.90192i −0.270164 + 0.0935876i
\(414\) −7.60770 −0.373898
\(415\) −5.59808 9.69615i −0.274799 0.475965i
\(416\) 1.73205 + 3.00000i 0.0849208 + 0.147087i
\(417\) 38.1962i 1.87047i
\(418\) −5.19615 3.00000i −0.254152 0.146735i
\(419\) −5.19615 9.00000i −0.253849 0.439679i 0.710734 0.703461i \(-0.248363\pi\)
−0.964582 + 0.263783i \(0.915030\pi\)
\(420\) 3.46410 + 3.00000i 0.169031 + 0.146385i
\(421\) 14.9904 25.9641i 0.730586 1.26541i −0.226046 0.974117i \(-0.572580\pi\)
0.956633 0.291296i \(-0.0940866\pi\)
\(422\) 17.8301 10.2942i 0.867957 0.501115i
\(423\) 13.5000 + 23.3827i 0.656392 + 1.13691i
\(424\) −3.63397 + 6.29423i −0.176481 + 0.305675i
\(425\) 0 0
\(426\) 4.09808 7.09808i 0.198552 0.343903i
\(427\) 11.1962 + 32.3205i 0.541820 + 1.56410i
\(428\) 13.7942 7.96410i 0.666769 0.384959i
\(429\) −14.1962 24.5885i −0.685397 1.18714i
\(430\) −2.76795 + 1.59808i −0.133482 + 0.0770661i
\(431\) 33.5885 + 19.3923i 1.61790 + 0.934094i 0.987463 + 0.157854i \(0.0504574\pi\)
0.630437 + 0.776241i \(0.282876\pi\)
\(432\) −5.19615 −0.250000
\(433\) 18.0000i 0.865025i −0.901628 0.432512i \(-0.857627\pi\)
0.901628 0.432512i \(-0.142373\pi\)
\(434\) 20.4904 7.09808i 0.983570 0.340719i
\(435\) 11.1962i 0.536814i
\(436\) −3.59808 + 6.23205i −0.172317 + 0.298461i
\(437\) −3.21539 −0.153813
\(438\) −6.00000 10.3923i −0.286691 0.496564i
\(439\) 29.6603i 1.41561i −0.706410 0.707803i \(-0.749686\pi\)
0.706410 0.707803i \(-0.250314\pi\)
\(440\) 4.73205 0.225592
\(441\) −19.5000 7.79423i −0.928571 0.371154i
\(442\) 0 0
\(443\) 9.00000i 0.427603i 0.976877 + 0.213801i \(0.0685846\pi\)
−0.976877 + 0.213801i \(0.931415\pi\)
\(444\) 10.7321 0.509321
\(445\) −4.39230 −0.208215
\(446\) −6.86603 + 11.8923i −0.325116 + 0.563117i
\(447\) 18.0000 10.3923i 0.851371 0.491539i
\(448\) 2.50000 0.866025i 0.118114 0.0409159i
\(449\) 9.58846i 0.452507i −0.974068 0.226254i \(-0.927352\pi\)
0.974068 0.226254i \(-0.0726478\pi\)
\(450\) 2.59808 + 1.50000i 0.122474 + 0.0707107i
\(451\) −36.8827 21.2942i −1.73674 1.00271i
\(452\) 10.9019 6.29423i 0.512783 0.296056i
\(453\) 7.26795 0.341478
\(454\) −14.1962 + 8.19615i −0.666258 + 0.384664i
\(455\) 3.00000 + 8.66025i 0.140642 + 0.405999i
\(456\) −2.19615 −0.102844
\(457\) 2.39230 0.111907 0.0559537 0.998433i \(-0.482180\pi\)
0.0559537 + 0.998433i \(0.482180\pi\)
\(458\) −7.03590 + 12.1865i −0.328766 + 0.569439i
\(459\) 0 0
\(460\) 2.19615 1.26795i 0.102396 0.0591184i
\(461\) 2.59808 4.50000i 0.121004 0.209586i −0.799160 0.601119i \(-0.794722\pi\)
0.920164 + 0.391533i \(0.128055\pi\)
\(462\) −20.4904 + 7.09808i −0.953299 + 0.330232i
\(463\) 1.30385 + 2.25833i 0.0605949 + 0.104954i 0.894731 0.446604i \(-0.147367\pi\)
−0.834137 + 0.551558i \(0.814034\pi\)
\(464\) −5.59808 3.23205i −0.259884 0.150044i
\(465\) 12.2942 7.09808i 0.570131 0.329165i
\(466\) 0.633975 + 1.09808i 0.0293683 + 0.0508674i
\(467\) −3.40192 5.89230i −0.157422 0.272663i 0.776516 0.630097i \(-0.216985\pi\)
−0.933938 + 0.357434i \(0.883652\pi\)
\(468\) −9.00000 5.19615i −0.416025 0.240192i
\(469\) 10.0000 3.46410i 0.461757 0.159957i
\(470\) −7.79423 4.50000i −0.359521 0.207570i
\(471\) −26.4904 15.2942i −1.22061 0.704721i
\(472\) 2.19615i 0.101086i
\(473\) 15.1244i 0.695419i
\(474\) −21.8827 12.6340i −1.00511 0.580298i
\(475\) 1.09808 + 0.633975i 0.0503832 + 0.0290887i
\(476\) 0 0
\(477\) 21.8038i 0.998330i
\(478\) −1.56218 2.70577i −0.0714524 0.123759i
\(479\) −5.19615 9.00000i −0.237418 0.411220i 0.722554 0.691314i \(-0.242968\pi\)
−0.959973 + 0.280094i \(0.909635\pi\)
\(480\) 1.50000 0.866025i 0.0684653 0.0395285i
\(481\) 18.5885 + 10.7321i 0.847561 + 0.489339i
\(482\) −1.66987 2.89230i −0.0760606 0.131741i
\(483\) −7.60770 + 8.78461i −0.346162 + 0.399714i
\(484\) −5.69615 + 9.86603i −0.258916 + 0.448456i
\(485\) 7.39230 4.26795i 0.335667 0.193798i
\(486\) 13.5000 7.79423i 0.612372 0.353553i
\(487\) −17.0000 + 29.4449i −0.770344 + 1.33427i 0.167031 + 0.985952i \(0.446582\pi\)
−0.937375 + 0.348323i \(0.886751\pi\)
\(488\) 12.9282 0.585232
\(489\) 14.5359 0.657336
\(490\) 6.92820 1.00000i 0.312984 0.0451754i
\(491\) −23.4904 + 13.5622i −1.06011 + 0.612053i −0.925462 0.378841i \(-0.876323\pi\)
−0.134644 + 0.990894i \(0.542989\pi\)
\(492\) −15.5885 −0.702782
\(493\) 0 0
\(494\) −3.80385 2.19615i −0.171143 0.0988096i
\(495\) −12.2942 + 7.09808i −0.552584 + 0.319035i
\(496\) 8.19615i 0.368018i
\(497\) −4.09808 11.8301i −0.183824 0.530654i
\(498\) 16.7942 9.69615i 0.752567 0.434495i
\(499\) 8.09808 14.0263i 0.362520 0.627903i −0.625855 0.779939i \(-0.715250\pi\)
0.988375 + 0.152037i \(0.0485832\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −18.0000 −0.804181
\(502\) 18.0000i 0.803379i
\(503\) 7.39230 0.329607 0.164803 0.986326i \(-0.447301\pi\)
0.164803 + 0.986326i \(0.447301\pi\)
\(504\) −5.19615 + 6.00000i −0.231455 + 0.267261i
\(505\) 11.1962 0.498222
\(506\) 12.0000i 0.533465i
\(507\) 0.866025 + 1.50000i 0.0384615 + 0.0666173i
\(508\) 11.3923 0.505452
\(509\) 4.79423 8.30385i 0.212500 0.368062i −0.739996 0.672611i \(-0.765173\pi\)
0.952496 + 0.304550i \(0.0985060\pi\)
\(510\) 0 0
\(511\) −18.0000 3.46410i −0.796273 0.153243i
\(512\) 1.00000i 0.0441942i
\(513\) 5.70577 3.29423i 0.251916 0.145444i
\(514\) −24.5885 14.1962i −1.08455 0.626165i
\(515\) 10.5000 6.06218i 0.462685 0.267131i
\(516\) −2.76795 4.79423i −0.121852 0.211054i
\(517\) 36.8827 21.2942i 1.62210 0.936519i
\(518\) 10.7321 12.3923i 0.471539 0.544487i
\(519\) 7.09808 12.2942i 0.311571 0.539657i
\(520\) 3.46410 0.151911
\(521\) −10.5000 + 18.1865i −0.460013 + 0.796766i −0.998961 0.0455727i \(-0.985489\pi\)
0.538948 + 0.842339i \(0.318822\pi\)
\(522\) 19.3923 0.848778
\(523\) 28.5788 16.5000i 1.24967 0.721495i 0.278623 0.960401i \(-0.410122\pi\)
0.971043 + 0.238906i \(0.0767888\pi\)
\(524\) −2.19615 + 3.80385i −0.0959394 + 0.166172i
\(525\) 4.33013 1.50000i 0.188982 0.0654654i
\(526\) 6.86603 + 11.8923i 0.299373 + 0.518529i
\(527\) 0 0
\(528\) 8.19615i 0.356692i
\(529\) −8.28461 14.3494i −0.360200 0.623885i
\(530\) 3.63397 + 6.29423i 0.157850 + 0.273404i
\(531\) −3.29423 5.70577i −0.142957 0.247609i
\(532\) −2.19615 + 2.53590i −0.0952153 + 0.109945i
\(533\) −27.0000 15.5885i −1.16950 0.675211i
\(534\) 7.60770i 0.329217i
\(535\) 15.9282i 0.688636i
\(536\) 4.00000i 0.172774i
\(537\) −36.8827 + 21.2942i −1.59161 + 0.918914i
\(538\) 15.5885 + 9.00000i 0.672066 + 0.388018i
\(539\) −12.2942 + 30.7583i −0.529550 + 1.32486i
\(540\) −2.59808 + 4.50000i −0.111803 + 0.193649i
\(541\) −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i \(-0.221681\pi\)
−0.939110 + 0.343617i \(0.888348\pi\)
\(542\) −3.29423 5.70577i −0.141499 0.245084i
\(543\) −20.0885 11.5981i −0.862078 0.497721i
\(544\) 0 0
\(545\) 3.59808 + 6.23205i 0.154125 + 0.266952i
\(546\) −15.0000 + 5.19615i −0.641941 + 0.222375i
\(547\) −2.79423 + 4.83975i −0.119473 + 0.206933i −0.919559 0.392952i \(-0.871454\pi\)
0.800086 + 0.599885i \(0.204787\pi\)
\(548\) −6.29423 + 3.63397i −0.268876 + 0.155236i
\(549\) −33.5885 + 19.3923i −1.43352 + 0.827643i
\(550\) 2.36603 4.09808i 0.100888 0.174743i
\(551\) 8.19615 0.349168
\(552\) 2.19615 + 3.80385i 0.0934745 + 0.161903i
\(553\) −36.4711 + 12.6340i −1.55091 + 0.537251i
\(554\) 20.9545 12.0981i 0.890271 0.513998i
\(555\) 5.36603 9.29423i 0.227775 0.394518i
\(556\) 19.0981 11.0263i 0.809939 0.467618i
\(557\) −28.3923 16.3923i −1.20302 0.694564i −0.241795 0.970327i \(-0.577736\pi\)
−0.961226 + 0.275763i \(0.911069\pi\)
\(558\) 12.2942 + 21.2942i 0.520456 + 0.901457i
\(559\) 11.0718i 0.468287i
\(560\) 0.500000 2.59808i 0.0211289 0.109789i
\(561\) 0 0
\(562\) 7.33013 12.6962i 0.309203 0.535555i
\(563\) −13.6077 −0.573496 −0.286748 0.958006i \(-0.592574\pi\)
−0.286748 + 0.958006i \(0.592574\pi\)
\(564\) 7.79423 13.5000i 0.328196 0.568453i
\(565\) 12.5885i 0.529600i
\(566\) −16.8564 −0.708528
\(567\) 4.50000 23.3827i 0.188982 0.981981i
\(568\) −4.73205 −0.198552
\(569\) 6.00000i 0.251533i −0.992060 0.125767i \(-0.959861\pi\)
0.992060 0.125767i \(-0.0401390\pi\)
\(570\) −1.09808 + 1.90192i −0.0459934 + 0.0796628i
\(571\) 21.6077 0.904254 0.452127 0.891954i \(-0.350665\pi\)
0.452127 + 0.891954i \(0.350665\pi\)
\(572\) −8.19615 + 14.1962i −0.342698 + 0.593571i
\(573\) 5.19615 + 3.00000i 0.217072 + 0.125327i
\(574\) −15.5885 + 18.0000i −0.650650 + 0.751305i
\(575\) 2.53590i 0.105754i
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) 20.7846 + 12.0000i 0.865275 + 0.499567i 0.865775 0.500433i \(-0.166826\pi\)
−0.000500448 1.00000i \(0.500159\pi\)
\(578\) 14.7224 8.50000i 0.612372 0.353553i
\(579\) 11.9545 20.7058i 0.496811 0.860502i
\(580\) −5.59808 + 3.23205i −0.232447 + 0.134204i
\(581\) 5.59808 29.0885i 0.232247 1.20679i
\(582\) 7.39230 + 12.8038i 0.306421 + 0.530737i
\(583\) −34.3923 −1.42438
\(584\) −3.46410 + 6.00000i −0.143346 + 0.248282i
\(585\) −9.00000 + 5.19615i −0.372104 + 0.214834i
\(586\) 14.1962 8.19615i 0.586438 0.338580i
\(587\) −15.4019 + 26.6769i −0.635705 + 1.10107i 0.350660 + 0.936503i \(0.385957\pi\)
−0.986365 + 0.164571i \(0.947376\pi\)
\(588\) 1.73205 + 12.0000i 0.0714286 + 0.494872i
\(589\) 5.19615 + 9.00000i 0.214104 + 0.370839i
\(590\) 1.90192 + 1.09808i 0.0783010 + 0.0452071i
\(591\) 35.4904 + 20.4904i 1.45988 + 0.842862i
\(592\) −3.09808 5.36603i −0.127330 0.220542i
\(593\) 13.3923 + 23.1962i 0.549956 + 0.952552i 0.998277 + 0.0586791i \(0.0186889\pi\)
−0.448321 + 0.893873i \(0.647978\pi\)
\(594\) −12.2942 21.2942i −0.504438 0.873713i
\(595\) 0 0
\(596\) −10.3923 6.00000i −0.425685 0.245770i
\(597\) 10.3923 6.00000i 0.425329 0.245564i
\(598\) 8.78461i 0.359229i
\(599\) 4.39230i 0.179465i −0.995966 0.0897324i \(-0.971399\pi\)
0.995966 0.0897324i \(-0.0286012\pi\)
\(600\) 1.73205i 0.0707107i
\(601\) −27.5885 15.9282i −1.12536 0.649725i −0.182594 0.983188i \(-0.558449\pi\)
−0.942763 + 0.333464i \(0.891783\pi\)
\(602\) −8.30385 1.59808i −0.338440 0.0651327i
\(603\) 6.00000 + 10.3923i 0.244339 + 0.423207i
\(604\) −2.09808 3.63397i −0.0853695 0.147864i
\(605\) 5.69615 + 9.86603i 0.231582 + 0.401111i
\(606\) 19.3923i 0.787759i
\(607\) −5.30385 3.06218i −0.215277 0.124290i 0.388485 0.921455i \(-0.372999\pi\)
−0.603761 + 0.797165i \(0.706332\pi\)
\(608\) 0.633975 + 1.09808i 0.0257111 + 0.0445329i
\(609\) 19.3923 22.3923i 0.785816 0.907382i
\(610\) 6.46410 11.1962i 0.261724 0.453319i
\(611\) 27.0000 15.5885i 1.09230 0.630641i
\(612\) 0 0
\(613\) 3.39230 5.87564i 0.137014 0.237315i −0.789351 0.613942i \(-0.789583\pi\)
0.926365 + 0.376627i \(0.122916\pi\)
\(614\) 23.7846 0.959869
\(615\) −7.79423 + 13.5000i −0.314294 + 0.544373i
\(616\) 9.46410 + 8.19615i 0.381320 + 0.330232i
\(617\) 15.8038 9.12436i 0.636239 0.367333i −0.146925 0.989148i \(-0.546938\pi\)
0.783164 + 0.621815i \(0.213604\pi\)
\(618\) 10.5000 + 18.1865i 0.422372 + 0.731570i
\(619\) 14.1962 8.19615i 0.570592 0.329431i −0.186794 0.982399i \(-0.559810\pi\)
0.757386 + 0.652968i \(0.226476\pi\)
\(620\) −7.09808 4.09808i −0.285066 0.164583i
\(621\) −11.4115 6.58846i −0.457929 0.264386i
\(622\) 15.8038i 0.633677i
\(623\) −8.78461 7.60770i −0.351948 0.304796i
\(624\) 6.00000i 0.240192i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 20.1962 0.807201
\(627\) −5.19615 9.00000i −0.207514 0.359425i
\(628\) 17.6603i 0.704721i
\(629\) 0 0
\(630\) 2.59808 + 7.50000i 0.103510 + 0.298807i
\(631\) 12.3923 0.493330 0.246665 0.969101i \(-0.420665\pi\)
0.246665 + 0.969101i \(0.420665\pi\)
\(632\) 14.5885i 0.580298i
\(633\) 35.6603 1.41737
\(634\) 20.5359 0.815585
\(635\) 5.69615 9.86603i 0.226045 0.391521i
\(636\) −10.9019 + 6.29423i −0.432289 + 0.249582i
\(637\) −9.00000 + 22.5167i −0.356593 + 0.892143i
\(638\) 30.5885i 1.21101i
\(639\) 12.2942 7.09808i 0.486352 0.280796i
\(640\) −0.866025 0.500000i −0.0342327 0.0197642i
\(641\) 2.78461 1.60770i 0.109985 0.0635001i −0.443998 0.896028i \(-0.646440\pi\)
0.553984 + 0.832528i \(0.313107\pi\)
\(642\) 27.5885 1.08883
\(643\) −16.2058 + 9.35641i −0.639093 + 0.368981i −0.784265 0.620426i \(-0.786960\pi\)
0.145172 + 0.989406i \(0.453626\pi\)
\(644\) 6.58846 + 1.26795i 0.259622 + 0.0499642i
\(645\) −5.53590 −0.217976
\(646\) 0 0
\(647\) −2.30385 + 3.99038i −0.0905736 + 0.156878i −0.907753 0.419506i \(-0.862203\pi\)
0.817179 + 0.576384i \(0.195537\pi\)
\(648\) −7.79423 4.50000i −0.306186 0.176777i
\(649\) −9.00000 + 5.19615i −0.353281 + 0.203967i
\(650\) 1.73205 3.00000i 0.0679366 0.117670i
\(651\) 36.8827 + 7.09808i 1.44555 + 0.278196i
\(652\) −4.19615 7.26795i −0.164334 0.284635i
\(653\) −43.1769 24.9282i −1.68964 0.975516i −0.954786 0.297294i \(-0.903916\pi\)
−0.734857 0.678222i \(-0.762751\pi\)
\(654\) −10.7942 + 6.23205i −0.422088 + 0.243692i
\(655\) 2.19615 + 3.80385i 0.0858108 + 0.148629i
\(656\) 4.50000 + 7.79423i 0.175695 + 0.304314i
\(657\) 20.7846i 0.810885i
\(658\) −7.79423 22.5000i −0.303851 0.877141i
\(659\) −33.2942 19.2224i −1.29696 0.748800i −0.317081 0.948398i \(-0.602703\pi\)
−0.979878 + 0.199599i \(0.936036\pi\)
\(660\) 7.09808 + 4.09808i 0.276292 + 0.159517i
\(661\) 13.1436i 0.511227i 0.966779 + 0.255613i \(0.0822774\pi\)
−0.966779 + 0.255613i \(0.917723\pi\)
\(662\) 8.00000i 0.310929i
\(663\) 0 0
\(664\) −9.69615 5.59808i −0.376284 0.217247i
\(665\) 1.09808 + 3.16987i 0.0425816 + 0.122922i
\(666\) 16.0981 + 9.29423i 0.623788 + 0.360144i
\(667\) −8.19615 14.1962i −0.317356 0.549677i
\(668\) 5.19615 + 9.00000i 0.201045 + 0.348220i
\(669\) −20.5981 + 11.8923i −0.796368 + 0.459783i
\(670\) −3.46410 2.00000i −0.133830 0.0772667i
\(671\) 30.5885 + 52.9808i 1.18085 + 2.04530i
\(672\) 4.50000 + 0.866025i 0.173591 + 0.0334077i
\(673\) 12.4904 21.6340i 0.481469 0.833928i −0.518305 0.855196i \(-0.673437\pi\)
0.999774 + 0.0212674i \(0.00677013\pi\)
\(674\) −8.66025 + 5.00000i −0.333581 + 0.192593i
\(675\) 2.59808 + 4.50000i 0.100000 + 0.173205i
\(676\) 0.500000 0.866025i 0.0192308 0.0333087i
\(677\) 22.9808 0.883222 0.441611 0.897207i \(-0.354407\pi\)
0.441611 + 0.897207i \(0.354407\pi\)
\(678\) 21.8038 0.837372
\(679\) 22.1769 + 4.26795i 0.851072 + 0.163789i
\(680\) 0 0
\(681\) −28.3923 −1.08800
\(682\) 33.5885 19.3923i 1.28617 0.742570i
\(683\) −30.7750 17.7679i −1.17757 0.679872i −0.222121 0.975019i \(-0.571298\pi\)
−0.955452 + 0.295148i \(0.904631\pi\)
\(684\) −3.29423 1.90192i −0.125958 0.0727219i
\(685\) 7.26795i 0.277694i
\(686\) 15.5885 + 10.0000i 0.595170 + 0.381802i
\(687\) −21.1077 + 12.1865i −0.805309 + 0.464945i
\(688\) −1.59808 + 2.76795i −0.0609261 + 0.105527i
\(689\) −25.1769 −0.959164
\(690\) 4.39230 0.167212
\(691\) 5.07180i 0.192940i 0.995336 + 0.0964701i \(0.0307552\pi\)
−0.995336 + 0.0964701i \(0.969245\pi\)
\(692\) −8.19615 −0.311571
\(693\) −36.8827 7.09808i −1.40106 0.269634i
\(694\) −21.2487 −0.806590
\(695\) 22.0526i 0.836501i
\(696\) −5.59808 9.69615i −0.212195 0.367532i
\(697\) 0 0
\(698\) −8.19615 + 14.1962i −0.310229 + 0.537332i
\(699\) 2.19615i 0.0830661i
\(700\) −2.00000 1.73205i −0.0755929 0.0654654i
\(701\) 44.3205i 1.67396i −0.547232 0.836981i \(-0.684318\pi\)
0.547232 0.836981i \(-0.315682\pi\)
\(702\) −9.00000 15.5885i −0.339683 0.588348i
\(703\) 6.80385 + 3.92820i 0.256612 + 0.148155i
\(704\) 4.09808 2.36603i 0.154452 0.0891729i
\(705\) −7.79423 13.5000i −0.293548 0.508439i
\(706\) −0.509619 + 0.294229i −0.0191798 + 0.0110734i
\(707\) 22.3923 + 19.3923i 0.842149 + 0.729323i
\(708\) −1.90192 + 3.29423i −0.0714787 + 0.123805i
\(709\) −46.7846 −1.75703 −0.878516 0.477712i \(-0.841466\pi\)
−0.878516 + 0.477712i \(0.841466\pi\)
\(710\) −2.36603 + 4.09808i −0.0887954 + 0.153798i
\(711\) −21.8827 37.9019i −0.820665 1.42143i
\(712\) −3.80385 + 2.19615i −0.142555 + 0.0823043i
\(713\) 10.3923 18.0000i 0.389195 0.674105i
\(714\) 0 0
\(715\) 8.19615 + 14.1962i 0.306519 + 0.530906i
\(716\) 21.2942 + 12.2942i 0.795803 + 0.459457i
\(717\) 5.41154i 0.202098i
\(718\) −7.90192 13.6865i −0.294897 0.510777i
\(719\) −20.7846 36.0000i −0.775135 1.34257i −0.934718 0.355389i \(-0.884348\pi\)
0.159583 0.987184i \(-0.448985\pi\)
\(720\) 3.00000 0.111803
\(721\) 31.5000 + 6.06218i 1.17312 + 0.225767i
\(722\) 15.0622 + 8.69615i 0.560556 + 0.323637i
\(723\) 5.78461i 0.215132i
\(724\) 13.3923i 0.497721i
\(725\) 6.46410i 0.240071i
\(726\) −17.0885 + 9.86603i −0.634212 + 0.366163i
\(727\) 41.7846 + 24.1244i 1.54971 + 0.894723i 0.998164 + 0.0605756i \(0.0192936\pi\)
0.551542 + 0.834147i \(0.314040\pi\)
\(728\) 6.92820 + 6.00000i 0.256776 + 0.222375i
\(729\) 27.0000 1.00000
\(730\) 3.46410 + 6.00000i 0.128212 + 0.222070i
\(731\) 0 0
\(732\) 19.3923 + 11.1962i 0.716760 + 0.413822i
\(733\) −29.4904 17.0263i −1.08925 0.628880i −0.155875 0.987777i \(-0.549820\pi\)
−0.933377 + 0.358897i \(0.883153\pi\)
\(734\) 14.5981 + 25.2846i 0.538825 + 0.933272i
\(735\) 11.2583 + 4.50000i 0.415270 + 0.165985i
\(736\) 1.26795 2.19615i 0.0467372 0.0809513i
\(737\) 16.3923 9.46410i 0.603818 0.348615i
\(738\) −23.3827 13.5000i −0.860729 0.496942i
\(739\) −16.5885 + 28.7321i −0.610216 + 1.05693i 0.380987 + 0.924580i \(0.375584\pi\)
−0.991204 + 0.132345i \(0.957749\pi\)
\(740\) −6.19615 −0.227775
\(741\) −3.80385 6.58846i −0.139738 0.242033i
\(742\) −3.63397 + 18.8827i −0.133407 + 0.693205i
\(743\) −23.6769 + 13.6699i −0.868622 + 0.501499i −0.866890 0.498499i \(-0.833885\pi\)
−0.00173176 + 0.999999i \(0.500551\pi\)
\(744\) 7.09808 12.2942i 0.260228 0.450728i
\(745\) −10.3923 + 6.00000i −0.380745 + 0.219823i
\(746\) 8.83013 + 5.09808i 0.323294 + 0.186654i
\(747\) 33.5885 1.22894
\(748\) 0 0
\(749\) 27.5885 31.8564i 1.00806 1.16401i
\(750\) −1.50000 0.866025i −0.0547723 0.0316228i
\(751\) 10.8038 18.7128i 0.394238 0.682840i −0.598766 0.800924i \(-0.704342\pi\)
0.993004 + 0.118084i \(0.0376752\pi\)
\(752\) −9.00000 −0.328196
\(753\) 15.5885 27.0000i 0.568075 0.983935i
\(754\) 22.3923i 0.815480i
\(755\) −4.19615 −0.152714
\(756\) −12.9904 + 4.50000i −0.472456 + 0.163663i
\(757\) −8.58846 −0.312153 −0.156076 0.987745i \(-0.549885\pi\)
−0.156076 + 0.987745i \(0.549885\pi\)
\(758\) 9.60770i 0.348967i
\(759\) −10.3923 + 18.0000i −0.377217 + 0.653359i
\(760\) 1.26795 0.0459934
\(761\) −16.5000 + 28.5788i −0.598125 + 1.03598i 0.394973 + 0.918693i \(0.370754\pi\)
−0.993098 + 0.117289i \(0.962579\pi\)
\(762\) 17.0885 + 9.86603i 0.619049 + 0.357408i
\(763\) −3.59808 + 18.6962i −0.130259 + 0.676846i
\(764\) 3.46410i 0.125327i
\(765\) 0 0
\(766\) −16.7942 9.69615i −0.606800 0.350336i
\(767\) −6.58846 + 3.80385i −0.237895 + 0.137349i
\(768\) 0.866025 1.50000i 0.0312500 0.0541266i
\(769\) −13.5000 + 7.79423i −0.486822 + 0.281067i −0.723255 0.690581i \(-0.757355\pi\)
0.236433 + 0.971648i \(0.424022\pi\)
\(770\) 11.8301 4.09808i 0.426328 0.147684i
\(771\) −24.5885 42.5885i −0.885532 1.53379i
\(772\) −13.8038 −0.496811
\(773\) 9.00000 15.5885i 0.323708 0.560678i −0.657542 0.753418i \(-0.728404\pi\)
0.981250 + 0.192740i \(0.0617373\pi\)
\(774\) 9.58846i 0.344650i
\(775\) −7.09808 + 4.09808i −0.254970 + 0.147207i
\(776\) 4.26795 7.39230i 0.153210 0.265368i
\(777\) 26.8301 9.29423i 0.962525 0.333429i
\(778\) −12.3564 21.4019i −0.442999 0.767296i
\(779\) −9.88269 5.70577i −0.354084 0.204430i
\(780\) 5.19615 + 3.00000i 0.186052 + 0.107417i
\(781\) −11.1962 19.3923i −0.400630 0.693911i
\(782\) 0 0
\(783\) 29.0885 + 16.7942i 1.03954 + 0.600177i
\(784\) 5.50000 4.33013i 0.196429